The company's flagship product, the D-Wave One, is built around a novel type of superconducting processor that uses quantum mechanics to massively accelerate computation. In 2010 Lockheed Martin purchased serial number 1, completing the historic world's first sale of a quantum computer.

However, there have been several articles written that call into question the claim that it is a quantum computer:

But experts are skeptical that D-Wave's quantum computer is really, well, quantum.
"If this were the real thing, we would know about it," says Christopher Monroe, a quantum-computing researcher at the University of Maryland, in College Park. He says D-Wave hasn't demonstrated "signatures" believed to be essential to quantum computers, such as entanglement, a coupling between qubits.

At a recent computing workshop the company claimed to have also found evidence for entanglement with systems of two and eight qubits. Entanglement is a requirement for its machine to truly operate as a quantum computer, but not proof that it does.

Are D-Wave Systems's claims that their machine is a quantum computer actually true?

Welcome to Skeptics! What would you consider an acceptable answer? I think this issue has been broadly thrashed out already. The company has been claiming the devices it produces are quantum computers, but by your own reading, has failed to provide independent scientists with verifiable evidence that this is true. I'm wondering what more there is to say...
– Oddthinking♦May 3 '13 at 15:38

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To reiterate what @Oddthinking said, this is going to be a really tough one to get a good answer for unless you define what you are looking for. From what I read the D-Wave systems are based on Adiabatic quantum computing as opposed to Quantum circuit which adds a layer of complication.
– rjziiMay 3 '13 at 16:03

@RobZ You have the beginning of an answer there Rob. I think by comparing the different styles, and possibilities you can give a decent answer that can educate people, and hopefully satisfy the question-asker. Personally I know next to nothing about Quantum Computing, so I would be interested in such an answer.
– WertilqMay 3 '13 at 16:05

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Found the Nature article I was looking for that was published by the company.
– rjziiMay 3 '13 at 16:06

1 Answer
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Yes in the sense that it uses quantum properties to perform computations, but no in the more general case since it is not a Turing machine (i.e. universal computer).

This answer is somewhat complicated by the fact that what the general public thinks of as a computer and what computer scientists formally define as a Turing machine. Turing machines are interesting from a mathematical standpoint since any computer algorithm can be run on a Turning machine and Turing machines can simulate one another which gives rise to the concept of Turing completeness.

The quantum equivalent to a conventional Turing machine (i.e. a desktop computer) requires the use of quantum circuits that allow for general algorithms to be run on it. In keeping with Turing completeness, conventional computers can actually simulate quantum computers that make use of quantum circuits.

The processor in the D-Wave One – codenamed Rainier – is designed to
perform a single mathematical operation called discrete optimization.

Along with,

Rainier solves optimization problems using quantum annealing (QA),
which is a class of problem solving approaches that use quantum
effects to help get better solutions, faster.

Right off the bat we know that the D-Wave is not going to be Turing complete since it can only perform a single mathematical operations which means that it is not a quantum computer in the general sense; however, what about the specific case?

When first introduced there was quite a bit of controversy that D-Wave was not taking advantage of quantum effects to actually solve problems. However, this partly resolved with their 2011 publication of "Quantum annealing with manufactured spins" in Nature which contains the following point of interest in the abstract,

Here we use quantum annealing to find the ground state of an
artificial Ising spin system comprising an array of eight
superconducting flux quantum bits with programmable spin–spin
couplings. We observe a clear signature of quantum annealing,
distinguishable from classical thermal annealing through the
temperature dependence of the time at which the system dynamics
freezes. Our implementation can be configured in situ to realize a
wide variety of different spin networks, each of which can be
monitored as it moves towards a low-energy configuration

The paper is quite interesting but the mathematics can be quite heavy at times as well though. The key point of the paper is summarized in the conclusion,

This brings us to our main conclusion: a programmable artificial spin
system manufactured as an integrated circuit can be used to implement
a quantum algorithm. The experiments presented here constitute a step
between understanding single-qubit annealing and understanding the
multi-qubit processes that could be used to find low-energy
configurations in a realistic adiabatic quantum processor. In addition
to its problem-solving potential, a system such as this also provides
an interesting test bed for investigating the physics of interacting
quantum spins, and is an important step in an ongoing investigation
into much more complex spin systems realized using this type of
architecture. Although our manufactured spin system is not yet a
universal quantum computer, by adding a new type of coupler between
the qubits, universal quantum computation would become possible.

“Our work seems to show that, from a purely physical point of view,
quantum effects play a functional role in information processing in
the D-Wave processor,” said Sergio Boixo, first author of the research
paper, who conducted the research while he was a computer scientist at
ISI and research assistant professor at USC Viterbi

Considering the pure annealing time, the performance for typical
(median) instances matches that of a highly optimised classical
annealing code on a high-end Intel CPU.

Meaning that as of right now, there might not be much advantage in using their device over a conventional computer. However, they go on to note that,

Quantum speedup can then be detected by comparing the scaling results
of the simulated classical and quantum annealers to experiments, as we
discuss in detail in the supplementary material. Going to even larger
problem sizes we soon approach the limits of classical computers.
Optimistically extrapolating using the observed scaling, the median
time to find the best solution for our test problem will increase
from milliseconds to minutes for 2048 variables, and months for 4096
variables, and the scaling might be much worse if fat tailed
distributions start to dominate, as we had previously observed for
other Monte Carlo algorithms [28, 29]. A quantum annealer showing
better scaling than classical algorithms for these problem sizes would
be an exciting breakthrough, validating the potential of quantum
information processing to outperform its classical counterpart.

Meaning that they still feel that for larger data sets their device is likely to be a superior performer over a standard computer for these types of problems.

So to summarize, in the general sense of the D-Wave One being a Turing machine, it is not which means that it is not a quantum computer in the strictest sense of the meaning. However, in the more general sense that the D-Wave One is using quantum effects to perform calculations, the answer appears to be yes.

our test problem will increase from milliseconds to minutes for 2048 variables -- What's the size of the computer at the moment? And how big do they predict it must be in order to "prove" the concept, i.e. get better performance that "its classical counterpart"?
– ChrisWJun 29 '13 at 0:39

@ChrisW - Not sure what you mean, the concept is proven but the performance issue is very complicated since a classical implementation might perform better in some cases but not in others.
– rjziiJun 29 '13 at 1:16

"Proof", as in "the proof is in the pudding". The last quote confuses me with units/dimensions: for example, how many is "2048 variables" when it's measured in "qbits" or whatever it is they advertise in their specifications? I thought the implication of the quote was that for some sufficiently large size of problem, the quantum approach would scale better: is large is that large size, and how far is the current implementation from being, therefore, consistently superior?
– ChrisWJun 29 '13 at 1:31

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Eh, the question of if the D-Wave is faster than a classical computer is still an open question. The big point of contention for a long time was if it really was using quantum effects or not and that's the question that's been solved.
– rjziiJun 29 '13 at 1:35